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In the case of the second order acceleration, two clouds are approaching, therefore the energy the charged particle gains comes from the energy of the clouds. In the case of the first order acceleration, the charged particle gains energy as it moves repeatedly through the shock front. The region before the shock front (upstream) moves at higher speed than ...

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Note You should clarify your statement from "...a charged particle cannot gain energy from a magnetic field..." to "...a charged particle cannot gain energy from a static magnetic field..." There is nothing wrong with energy transfer from time-varying magnetic fields. Background If the spatial gradient in the magnetic field is slow enough such that the ...

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In principle, the answer should be yes. At any given temperature, the particles will have a distribution of speeds. Those in the tail of the distribution might have enough energy to fuse. However, the probability of this event would be extremely low because the number of particles with the required (HIGH!) energy is very low.

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In answer to your question, for the general purposes of plasma physics, $k_b$ is defined in $eV/K$, or electron volts per kelvin. You will sometimes see reference to the electron temperature being in units of $eV$ rather than $K$, but this is a simplified way of writing the temperature to deal with scales on the order of 10^4 $K$. In other words, it is ...

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So I actually integrated this a while ago, I thought I should share the result. It turned out rather simple with the right substitution. By the way I'm talking about both potential and charge disrtibution as a Debye-like. Point charge is straight forward... First we put the center of the charge density on the z-axis as mentioned in my question. I get  ...

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